A revised density split statistic model for general filters

Studying the statistical properties of large-scale structure in Universe with weak gravitational lensing is a prime goal several current and forthcoming galaxy surveys. The power that has to constrain cosmological parameters can be enhanced by considering statistics beyond second-order shear correlation functions or spectra. One such higher-order probe proven successful observational data density split (DSS), which one analyses mean profiles around points are classified according their foreground density. In this paper, we generalise most accurate DSS model allow for broad class angular filter used classification different local regions. This approach motivated earlier findings showing an optimised provide tighter constraints on compared standard top-hat case. We build large deviation theory approaches approximations thereof matter PDF, perturbative calculations moments field. novel addition relies generalisation these previously employed general validated sets numerical simulations. revised fits well simulation measurements, residual systematic offset small accuracy slightly lower compensated than non-negative function, it increases size. Using Fisher matrix approach, find comparable commonly two-point cosmic measures. Hence, our competitive data, while may need refinements